The diameter and height of a cylinder are mea | vedclass

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(B) The volume $V$ of a cylinder is given by $V = \pi R^2 h = \frac{\pi}{4} D^2 h$.Given $D = 12.6\, cm$,$\Delta D = 0.1\, cm$,$h = 34.2\, cm$,and $\D

Vedclass · Accepted Answer

$4260 \pm 80\, cm^3$

Vedclass · Answer

(B) The volume $V$ of a cylinder is given by $V = \pi R^2 h = \frac{\pi}{4} D^2 h$.Given $D = 12.6\, cm$,$\Delta D = 0.1\, cm$,$h = 34.2\, cm$,and $\Delta h = 0.1\, cm$.First,calculate the volume: $V = \frac{3.14159}{4} 	imes (12.6)^2 	imes 34.2 \approx 4264.4\, cm^3$.Rounding to appropriate significant figures (three significant figures based on the given data),$V = 4260\, cm^3$.Now,calculate the relative error: $\frac{\Delta V}{V} = 2\frac{\Delta D}{D} + \frac{\Delta h}{h}$.$\Delta V = V 	imes (2 	imes \frac{0.1}{12.6} + \frac{0.1}{34.2}) = 4264.4 	imes (0.01587 + 0.00292) \approx 4264.4 	imes 0.01879 \approx 80.13$.Rounding the absolute error to one significant figure,we get $\Delta V = 80\, cm^3$.Thus,the volume is $V = 4260 \pm 80\, cm^3$.

List $I$	List $II$
$A$. Torque	$I$. $[M^1 L^1 T^{-2} A^{-2}]$
$B$. Magnetic field	$II$. $[L^2 A^1]$
$C$. Magnetic moment	$III$. $[M^1 T^{-2} A^{-1}]$
$D$. Permeability of free space	$IV$. $[M^1 L^2 T^{-2}]$

List-$I$	List-$II$
$(a)$ ${R}_{H}$ (Rydberg constant)	$(i)$ ${kg} {m}^{-1} {s}^{-1}$
$(b)$ $h$ (Planck's constant)	$(ii)$ ${kg} {m}^{2} {s}^{-1}$
$(c)$ $u_{B}$ (Magnetic field energy density)	$(iii)$ ${m}^{-1}$
$(d)$ $\eta$ (Coefficient of viscosity)	$(iv)$ ${kg} {m}^{-1} {s}^{-2}$

The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\, cm$ and $34.2 \pm 0.1\, cm$,respectively. What will be the value of its volume in appropriate significant figures?

Similar Questions

The two principal thrusts in physics are

Identify the pair that has the same dimensions.

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$

$B$. Magnetic field $II$. $[L^2 A^1]$

$C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$

$D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$

Choose the correct answer from the options given below:

State,for each of the following physical quantities,if it is a scalar or a vector: volume,mass,speed,acceleration,density,number of moles,velocity,angular frequency,displacement,angular velocity.

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